Worksheet: Rearranging Formulas for Physical Quantities

In this worksheet, we will practice changing the subject of a formula and recognising valid rearrangements of combinations of formulas.

Q1:

One side of the formula 𝑣=𝑢+2𝑎𝑠 is 𝑣. The formula is rearranged so that one side of the formula is equal to (𝑣𝑢)2𝑠. Which of the following is the other side of the formula equal to?

  • A𝑎
  • B𝑎
  • C𝑎
  • D𝑎

Q2:

Kinetic energy is given by the formula 𝐸=12𝑚𝑣. The weight, 𝑊, of an object is 𝑚𝑔. Which of the following is a correct formula that has a subject equal to the ratio of the kinetic energy of an object to its weight?

  • A𝐸𝑊=𝑔2𝑣
  • B𝐸𝑊=2𝑣𝑔
  • C𝐸𝑊=𝑣2𝑔
  • D𝐸𝑊=2𝑔𝑣
  • E𝐸𝑊=𝑔𝑣2

Q3:

The subject of the formula forcemassacceleration=× is force. Which of the following correctly shows the same formula with acceleration as the subject of the formula?

  • AAccelerationmassforce=
  • BAccelerationforcemass=×
  • CAccelerationforcemass=

Q4:

The subject of the formula speeddistancetime= is speed. Which of the following correctly shows the same formula with time as the subject of the formula?

  • ATimedistancespeed=
  • BTimedistancespeed=×
  • CTimespeeddistance=

Q5:

The subject of the formula accelerationnalvelocityinitialvelocitytime=() is acceleration. Which of the following correctly shows the same formula with time as the subject of the formula?

  • ATimenalvelocityinitialvelocityacceleration=()
  • BTimenalvelocityinitialvelocityacceleration=()×
  • CTimeaccelerationnalvelocityinitialvelocity=()

Q6:

The subject of the formula for the volume of a cube, volumesidelength=, is volume. Which of the following correctly shows the same formula with side length as the subject of the formula?

  • ASidelengthvolume=
  • BSidelengthvolume=
  • CSidelengthvolume=1

Q7:

The momentum of an object is given by the formula momentummassvelocity=×, expressed in symbols as 𝑝=𝑚𝑣. The velocity of an object is given by the formula velocitydisplacementtime=, expressed in symbols as 𝑣=𝑠𝑡. Which of the following is a correct formula?

  • A𝑝𝑡=𝑚𝑠
  • B𝑝𝑡=𝑣𝑠
  • C𝑝𝑠=𝑚𝑡
  • D𝑝𝑣=𝑚𝑠
  • E𝑝𝑣=𝑚𝑡

Q8:

Gravitational potential energy is given by the formula 𝐸=𝑚𝑔, where 𝐸 is the energy, 𝑚 is the mass, 𝑔 is the acceleration due to gravity, and is the height. Acceleration is given by the formula accelerationchangeinvelocitytime=, written in symbols as 𝑎=Δ𝑣𝑡. Which of the following is a correct formula?

  • A=𝑚Δ𝑣𝑡𝐸
  • B=𝐸𝑚𝑡Δ𝑣
  • C=𝐸Δ𝑣𝑡𝑚
  • D=𝐸𝑡𝑚Δ𝑣
  • E=Δ𝑣𝑡𝐸𝑚

Q9:

The subject of the formula accelerationnalvelocityinitialvelocitytime=() is acceleration. Which of the following correctly shows the same formula with final velocity as the subject of the formula?

  • AFinalvelocityaccelerationtimeinitialvelocity=(×)
  • BFinalvelocityinitialvelocitytimeacceleration=()×
  • CFinalvelocityaccelerationtimeinitialvelocity=(×)+
  • DFinalvelocityinitialvelocitytimeacceleration=(×)+
  • EFinalvelocityaccelerationinitialvelocitytime=()

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